CN1639556B - Method for determining the elasto-plastic behavior of parts made of an anisotropic material, and use of said method - Google Patents
Method for determining the elasto-plastic behavior of parts made of an anisotropic material, and use of said method Download PDFInfo
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- CN1639556B CN1639556B CN038054027A CN03805402A CN1639556B CN 1639556 B CN1639556 B CN 1639556B CN 038054027 A CN038054027 A CN 038054027A CN 03805402 A CN03805402 A CN 03805402A CN 1639556 B CN1639556 B CN 1639556B
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- 239000000463 material Substances 0.000 title claims abstract description 21
- 238000000034 method Methods 0.000 title claims abstract description 19
- 238000012937 correction Methods 0.000 claims abstract description 9
- 239000011159 matrix material Substances 0.000 claims abstract 2
- 230000000052 comparative effect Effects 0.000 claims description 6
- 239000013078 crystal Substances 0.000 claims description 4
- 125000004122 cyclic group Chemical group 0.000 claims description 4
- 238000012804 iterative process Methods 0.000 claims 1
- 238000009434 installation Methods 0.000 abstract 1
- 238000012360 testing method Methods 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 230000001419 dependent effect Effects 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 229910001011 CMSX-4 Inorganic materials 0.000 description 1
- 230000005483 Hooke's law Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000002485 combustion reaction Methods 0.000 description 1
- 238000005260 corrosion Methods 0.000 description 1
- 230000007797 corrosion Effects 0.000 description 1
- 230000001186 cumulative effect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 239000013013 elastic material Substances 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000009661 fatigue test Methods 0.000 description 1
- 238000009472 formulation Methods 0.000 description 1
- 230000014509 gene expression Effects 0.000 description 1
- 238000011835 investigation Methods 0.000 description 1
- 239000004973 liquid crystal related substance Substances 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 230000003647 oxidation Effects 0.000 description 1
- 238000007254 oxidation reaction Methods 0.000 description 1
- 238000003825 pressing Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 239000013589 supplement Substances 0.000 description 1
- 238000005050 thermomechanical fatigue Methods 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/60—Investigating resistance of materials, e.g. refractory materials, to rapid heat changes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/02—Details
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0001—Type of application of the stress
- G01N2203/0005—Repeated or cyclic
- G01N2203/0007—Low frequencies up to 100 Hz
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0092—Visco-elasticity, solidification, curing, cross-linking degree, vulcanisation or strength properties of semi-solid materials
- G01N2203/0094—Visco-elasticity
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/0202—Control of the test
- G01N2203/0212—Theories, calculations
- G01N2203/0218—Calculations based on experimental data
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/022—Environment of the test
- G01N2203/0222—Temperature
- G01N2203/0226—High temperature; Heating means
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/022—Environment of the test
- G01N2203/0244—Tests performed "in situ" or after "in situ" use
- G01N2203/0246—Special simulation of "in situ" conditions, scale models or dummies
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- General Health & Medical Sciences (AREA)
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- Life Sciences & Earth Sciences (AREA)
- Chemical & Material Sciences (AREA)
- Analytical Chemistry (AREA)
- Biochemistry (AREA)
- Health & Medical Sciences (AREA)
- General Physics & Mathematics (AREA)
- Physics & Mathematics (AREA)
- Pathology (AREA)
- Turbine Rotor Nozzle Sealing (AREA)
- Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
- Testing Resistance To Weather, Investigating Materials By Mechanical Methods (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
- Extrusion Moulding Of Plastics Or The Like (AREA)
Abstract
Disclosed is a method for determining the elasto-plastic behavior of parts, particularly gas turbine installations, at high temperatures, according to which the linear elastic behavior is determined first while also taking into account the inelastic behavior on the basis of the linear elastic results by applying Neuber's rule. The anisotropic properties of the parts, which appear particularly by using monocrystalline materials, are taken into account in a simple manner by a modified anisotropic Neuber's rule of form (I): sigma*2=sigmaep2[1+(A/C)(a/ER)[Asigmaep2/sigma02]n-1], in which A = inelastic anisotropic correction term, A=1/2[F(Dyy-Dzz)<2>+G(Dzz-Dxx)<2>+H(Dxx-Dyy)<2>+2LDyz<2>+2MDzx<2>+2NDxy<2>], F, G, H, L, M, and N representing the Hill constants, C = elastic anisotropic correctionterm, C=D.E-1.D, sigma* = detected linear stress, sigmaep = estimated inelastic stress, D = directional vector of the elastic and inelastic stresses, E-1= inverse stiffness matrix, ER = reference stiffness, sigma0 = reference stress, and alpha, n = material constants.
Description
Technical Field
The present invention relates to the field of analysis and prediction of mechanical component characteristics. The invention relates to a method for determining the elastic-plastic properties of components, in particular of gas turbine plants, at high temperatures.
Background
The components (rotor blades, stator blades, linings, etc.) of gas turbines are often subjected to high loads, so that their service life is limited. Predicting such service life is essential to reliably and economically designing a gas turbine.
The loads on these components consist of forces, high thermal loads, oxidation and corrosion. Mechanical and thermal loading in many cases leads to component fatigue after several thousand load cycles. This Low Cycle Fatigue is described by Low Cycle Fatigue tests (LCF) at isothermal conditions and by thermo-Mechanical Fatigue Tests (TMF) at isothermal conditions.
During the design phase of the gas turbine, the stresses caused by the load are calculated. The complexity of the geometry and/or the loading requires the stress to be calculated using finite element method (FE). However, since the necessary inelastic calculations are generally not possible for cost and time reasons, the prediction of the service life can be carried out almost exclusively on the basis of linear-elastic stresses. In most cases only isothermal data (examination of extended LCF tests) are available, so that the LCF data must also be used for the anisothermal evaluation.
In this respect, the total contrast extension εv，epThe magnitude of (c) is used as the degree of damage (law of damage). If the required number of cycles N on the part is reachedreqThen the total comparative elongation ε at each portion of the partv，epMust satisfy the relation
εa MIs the allowable total elongation amplitude determined from isothermal LCF tests. It should be determined for different temperatures and cycle numbers. Temperature T on damage basisdamIt must be properly selected for one cycle of temperature change.
If the standard load is applied for many minutes at high temperature, additional damage should be taken into account. To understand the cumulative reduction in service life based on damage from creep fatigue and cyclic fatigue, LCF data were measured in a test with hold time.
Extent of damage εv，epCorresponding to the degree of elongation of one action cycle. This cycle was determined from the cycle of the linear-elastic analysis by a modified Neuber-rule.
Wherein,
σ *devin order to measure the error of the linear stress,
ε *(σ *dev) For the purpose of measuring the linear elongation,
σ ep deverror for estimated elastic-plastic stress and
ε ep(σ dev) Is the vector of the magnitude of elastic-plastic elongation.
Extent of damage εv，epAssuming by comparison the magnitude of elongation from total elasticity-plasticityε ep(σ dev) Is determined.
For determining the magnitude of the total elastic-plastic elongationεep(σ dev) The required cyclicity σ - ε -curve is analytically represented by a modified Ramberg-Osgood-relation.
The inelastic effects occurring in the gas turbine components (blades, combustion chambers) can then be approximated by means of the Neuber rule. These effects must be considered in the prediction of the useful life of the structure. However, only the Neuber's-rule (b) for isotropic mechanical materials is known to date.
Since, owing to their special properties in gas turbine production, the use of (anisotropic) monocrystalline materials is increasing in particular for turbine blade parts, it is desirable for the design of these parts, in particular in the determination of the service life under cyclic loading, to provide a calculation method which is similar to that of isotropic materials.
Disclosure of Invention
The object of the present invention is therefore to provide a method for the approximate determination of the elastic-plastic properties of monocrystalline materials at high temperatures, in particular for the determination of the service life of gas turbine plant components made of monocrystalline materials.
The core of the invention is that, in order to take account of the anisotropic properties of the component, in particular produced by using a monocrystalline material, the anisotropic Neuber rule is modified in the following manner
In this respect, the numerical values are preferredσ *devAndσ ep devusing the following relation
And
in this regard, in the case of a liquid crystal display,D＝[Dxx，Dyy，Dzz，Dyz，Dzx，Dxy]is a vector of length 1 and is,D T D1, additionally having a bias, Dxx+Dyy+Dzz1. Furthermore, the relational expressions are appliedσ *·σ *＝σ*2Andσ ep·σ ep＝σep 2from which the modified Neuber-rule is derived, which can be expressed in the following way
Adding anisotropic inelastic correction terms
And anisotropic elastic correction term
Wherein F, G, H, L, M and N are Hill parameters.
According to a preferred embodiment of the method, the equation-modified Neuber rule is solved using an iterative method, in particular Newton-iteration.
According to the invention, the method is used to determine the service life of a gas turbine component under cyclic load.
Detailed Description
The material model on which the invention is based is deduced from the plastic potential:
in this case
-ERFor 'reference' -rigidity. Substitution into ERIn order to obtain a formal similarity of the formula to that of the well-known isotropic case. ERChosen according to purpose in the order of magnitude of the correction term for elasticity of the material under investigation, e.g. ER＝100000Nmm2，
Omega is the plastic potential of the material, from which the plastic elongation is calculated by deduction as a stress,
-σ0for the 'reference' -stress, chosen in the order of the yield point according to the purpose, and
-σv，epcomparative stress for anisotropy (see below).
Plastic elongation and then formation
By pressing stress from the potential of plasticityσ epLocal development of plastic elongationε pl。
Using equations (1) and (2) to arrive at
σv，epThe stresses are compared (anisotropically). In the present anisotropic case, the comparative stress per HILL can be used:
for the general case of orthotropic materials, six dependent plastic material constants F, G, H and L, M and N (Hill constants) should be considered. The special case of 1 ═ F ═ G ═ H ═ 3L ═ 3M ═ 3N results in the well-known von-Mises comparative stress of isotropic materials; the special case of two dependent parameters F ═ G ═ H and L ═ M ═ N yields a formulation of the cubic crystal symmetry, which is notable here for single-crystal materials (e.g. CMSX-4).
From equation (3) follows
Add 'vector'
And 'comparative elongation'
Using the linear-elastic equation for single crystal materials with cubic symmetry of note here
Three function-elastic material constants for symmetric (single crystal-) materials.
Complete anisotropic Ramberg-Osgood Material Law as a sum of elastic and Plastic elongation Generation
In a variation of the Neuber's rule used here, the manner of modifying the linear elastic and elastic plastic values works equally well
Elastic plastic elongationε ep(σ dev) The deviation value is shown in the Ramberg-Osgood-relation
Linear elastic elongation epsilon*(σ*dev) Generated from Hooke's Law in the following manner
Thus obtaining the anisotropic Neuber's rule
It is assumed here that the elastic-plastic stress is proportional to the elastic stress (calculated from finite elements). Or in other words if it is assumed from the elastic stress σ*Stress in the stress space if transitioning to an estimated inelastic stressThe direction is unchanged. The 'vector' D can be determined therefrom
(14) <math><mrow><msup><munder><mi>σ</mi><mo>‾</mo></munder><mrow><mo>*</mo><mi>dev</mi></mrow></msup><munder><mi>D</mi><mo>‾</mo></munder><msqrt><msup><mi>σ</mi><mrow><mo>*</mo><mn>2</mn></mrow></msup></msqrt></mrow></math>
For inelastic (estimated) stresses, the same vector now applies
Thereby generating elastic stress
And is produced for inelastic stress
For elastic-plastic comparative stress
Therefore, equation (13) can also be expressed in the following manner
Adding anisotropic inelastic correction terms
Anisotropic elastic correction term
Equation (19) σ aboveep 2Iterative solutions (Newton-iteration) can be used as in the case of the 'traditional' Neuber rule. If σ isep 2Determination may then be made byDThe elasto-plastic stress vector is immediately calculated.
To supplement the 'linear' results of the finite element calculations, the above steps are performed, depending on the purpose, in a Post-Processing-program which reads the 'linear' data of elongation and stress from the FE-program memory and further processes these data into the desired inelastic results. In the case of the isotropic Neuber rule, this is prior art. By adding the two ' correction factors ' described above to the iteration step, it is very easy to extend to the anisotropic Neuber's rule described herein.
Claims (5)
1. Method for determining the elastic-plastic properties of a component of a gas turbine plant at high temperatures, in which method first the linear-elastic properties are determined and on the basis of the linear-elastic results the inelastic properties are simultaneously taken into account by using the Neuber rule, characterized in that, in order to take account of the anisotropic properties occurring by using a single crystal material for the component, the following formal modified anisotropic Neuber rule is used
Wherein
σ *devThe error in the measured linear stress,
ε *(σ*dev) The linear elongation measured is the linear elongation measured,
σ ep devthe error of the estimated elastic-plastic stress,
σv，cphill elastic-plastic comparative stress
ERReference-rigidity
σ0As the standard stress, the stress is,
α, n is constant, and
σ epestimated elastic-plastic stress.
2. The method of claim 1, wherein the value is a numerical valueσ *devAndσ ep devgiven the following relation
And
whereinσ ep·σ ep＝σep 2Where D is a length 1 vector with bias properties, the Neuber's rule is modified in the following manner
Adding anisotropic inelastic correction terms
And anisotropic elastic correction term
Wherein F, G, H, L, M and N are Hill parameters.
3. The method of claim 2, wherein the equation is solved using an iterative method according to a modified Neuber's rule.
4. Use of the method according to any of claims 1-3 for determining the service life of a gas turbine component under cyclic load.
5. The method of claim 3, wherein said iterative process is a Newton-iteration.
Applications Claiming Priority (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CH00402/02A CH695515A5 (en) | 2002-03-08 | 2002-03-08 | A method for determining the elasto-plastic behavior of consisting of anisotropic material components and use of the method. |
| CH402/02 | 2002-03-08 | ||
| CH402/2002 | 2002-03-08 | ||
| PCT/CH2003/000135 WO2003076908A1 (en) | 2002-03-08 | 2003-02-21 | Method for determining the elasto-plastic behavior of parts made of an anisotropic material, and use of said method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN1639556A CN1639556A (en) | 2005-07-13 |
| CN1639556B true CN1639556B (en) | 2010-04-28 |
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| Application Number | Title | Priority Date | Filing Date |
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| CN038054027A Expired - Fee Related CN1639556B (en) | 2002-03-08 | 2003-02-21 | Method for determining the elasto-plastic behavior of parts made of an anisotropic material, and use of said method |
Country Status (7)
| Country | Link |
|---|---|
| US (1) | US7050912B2 (en) |
| EP (1) | EP1483563B1 (en) |
| JP (1) | JP2005519300A (en) |
| CN (1) | CN1639556B (en) |
| AU (1) | AU2003205492A1 (en) |
| CH (1) | CH695515A5 (en) |
| WO (1) | WO2003076908A1 (en) |
Families Citing this family (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CH695515A5 (en) | 2002-03-08 | 2006-06-15 | Alstom Technology Ltd | A method for determining the elasto-plastic behavior of consisting of anisotropic material components and use of the method. |
| US7613585B1 (en) * | 2005-12-05 | 2009-11-03 | Livermore Software Technology Corporation | Method and system for defining material properties hierarchically in finite element analysis |
| US8108156B2 (en) * | 2008-11-06 | 2012-01-31 | GM Global Technology Operations LLC | Methods, program products, and systems for estimating the stress-strain relationship of a toughened structural adhesive polymer |
| JP5025676B2 (en) * | 2009-03-25 | 2012-09-12 | 株式会社東芝 | Monitoring device and monitoring method |
| US9194376B2 (en) * | 2011-05-24 | 2015-11-24 | General Electric Company | System and method for estimating remaining life for a device |
| FR2999290B1 (en) * | 2012-12-12 | 2016-01-01 | Areva | METHOD AND DEVICE FOR ULTRASONIC VOLUMIC CONTROL OF THE PRESENCE OF DEFECTS IN A WELDING |
| CN103091167B (en) * | 2013-01-23 | 2014-10-29 | 西北工业大学 | Method for continuously measuring change of shrinkage strain ratio of titanium alloy pipe |
| CN104316388B (en) * | 2014-07-25 | 2016-09-28 | 中国航空工业集团公司北京航空材料研究院 | One carries out method for measuring fatigue life to anisotropic material structural member |
| CN105718735B (en) * | 2016-01-22 | 2021-06-11 | 中国建筑第八工程局有限公司 | Soil plasticity accumulation model under high cycle cyclic load |
| CN106802202B (en) * | 2017-03-15 | 2019-04-12 | 哈尔滨工业大学 | A method of measurement anisotropic material plane stress |
| CN107220430B (en) * | 2017-05-24 | 2019-12-10 | 中南大学 | Method for calculating stress distribution of steel wire layer of woven hydraulic rubber hose in vibration environment |
| CN108009370B (en) * | 2017-12-13 | 2021-08-17 | 中国飞机强度研究所 | Structural stress sensitivity solving method |
| CN108416084B (en) * | 2018-01-23 | 2022-02-18 | 南京理工大学 | Elastoplasticity damage finite element method considering elastoplasticity and damage coupling of composite material |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1995031715A1 (en) * | 1994-05-18 | 1995-11-23 | Fatigue Management Associates L.L.C. | Method for measuring and extending the service life of fatigue-limited metal components |
| US5736645A (en) * | 1997-01-16 | 1998-04-07 | Ford Global Technologies, Inc. | Method of predicting crack initiation based fatigue life |
| DE10118542A1 (en) * | 2001-04-14 | 2002-10-17 | Alstom Switzerland Ltd | Method for determining the elasto-plastic behavior of components consisting of anisotropic material and application of the method |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CH695515A5 (en) | 2002-03-08 | 2006-06-15 | Alstom Technology Ltd | A method for determining the elasto-plastic behavior of consisting of anisotropic material components and use of the method. |
-
2002
- 2002-03-08 CH CH00402/02A patent/CH695515A5/en not_active IP Right Cessation
-
2003
- 2003-02-21 AU AU2003205492A patent/AU2003205492A1/en not_active Abandoned
- 2003-02-21 WO PCT/CH2003/000135 patent/WO2003076908A1/en active Application Filing
- 2003-02-21 EP EP03702264.7A patent/EP1483563B1/en not_active Expired - Lifetime
- 2003-02-21 JP JP2003575083A patent/JP2005519300A/en not_active Withdrawn
- 2003-02-21 CN CN038054027A patent/CN1639556B/en not_active Expired - Fee Related
-
2004
- 2004-09-08 US US10/935,167 patent/US7050912B2/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1995031715A1 (en) * | 1994-05-18 | 1995-11-23 | Fatigue Management Associates L.L.C. | Method for measuring and extending the service life of fatigue-limited metal components |
| US5736645A (en) * | 1997-01-16 | 1998-04-07 | Ford Global Technologies, Inc. | Method of predicting crack initiation based fatigue life |
| DE10118542A1 (en) * | 2001-04-14 | 2002-10-17 | Alstom Switzerland Ltd | Method for determining the elasto-plastic behavior of components consisting of anisotropic material and application of the method |
Non-Patent Citations (6)
| Title |
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| 曾海泉等.基于局部应力应变法的寿命预测系统.沈阳化工学院学报11 1.1997,11(1),41-46. |
| 曾海泉等.基于局部应力应变法的寿命预测系统.沈阳化工学院学报11 1.1997,11(1),41-46. * |
| 田秀云,杜洪增,王忠义.铆接薄壁梁疲劳寿命计算与试验分析.航空学报20 5.1999,20(5),471-474. |
| 田秀云,杜洪增,王忠义.铆接薄壁梁疲劳寿命计算与试验分析.航空学报20 5.1999,20(5),471-474. * |
| 高庆 赵永翔 谷芳毓.基于虚拟应力幅的低周疲劳可靠性分析.核动力工程21 1.2000,21(1),88-93. |
| 高庆 赵永翔 谷芳毓.基于虚拟应力幅的低周疲劳可靠性分析.核动力工程21 1.2000,21(1),88-93. * |
Also Published As
| Publication number | Publication date |
|---|---|
| JP2005519300A (en) | 2005-06-30 |
| EP1483563A1 (en) | 2004-12-08 |
| US20050065749A1 (en) | 2005-03-24 |
| US7050912B2 (en) | 2006-05-23 |
| CH695515A5 (en) | 2006-06-15 |
| EP1483563B1 (en) | 2015-12-30 |
| WO2003076908A1 (en) | 2003-09-18 |
| CN1639556A (en) | 2005-07-13 |
| AU2003205492A1 (en) | 2003-09-22 |
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